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Example 31.23.2. Let $A = \mathbf{C}[x, \{ y_\alpha \} _{\alpha \in \mathbf{C}}]/ ((x - \alpha )y_\alpha , y_\alpha y_\beta )$. Any element of $A$ can be written uniquely as $f(x) + \sum \lambda _\alpha y_\alpha $ with $f(x) \in \mathbf{C}[x]$ and $\lambda _\alpha \in \mathbf{C}$. Let $X = \mathop{\mathrm{Spec}}(A)$. In this case $\mathcal{O}_ X = \mathcal{K}_ X$, since on any affine open $D(f)$ the ring $A_ f$ any nonzerodivisor is a unit (proof omitted).


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